DnD3 Attacks 3
power critical
In my previous DnD3 Attacks post, I showed the odds for scoring critcal hits with various threat ranges. One situation that isn't covered by that data is the Power Critical feat from the Complete Warrior supplement.
The unique thing of Power Critical and similar tweaks is that it adds a bonus for confirming critical hits only, without changing the threat range or the original attack bonus. In this case, it's a +4 bonus to confirm. This results in a four-step shift of the critical odds in the tables of the previous post, with two caveats. First, you can't improved beyond the hit-on-a-two case, so that puts a cap on the top end of the chart. Second, once again threat decline makes the odds at the bottom of the graph decrease faster.
Here is a comparison between the odds for threat 15–20 both with and without Power Critical, using this slightly modified AnyDice program.
| needed | no PC | with PC |
|---|---|---|
| 2 | 28.50% | 28.50% |
| 3 | 27.00% | 28.50% |
| 4 | 25.50% | 28.50% |
| 5 | 24.00% | 28.50% |
| 6 | 22.50% | 28.50% |
| 7 | 21.00% | 27.00% |
| 8 | 19.50% | 25.50% |
| 9 | 18.00% | 24.00% |
| 10 | 16.50% | 22.50% |
| 11 | 15.00% | 21.00% |
| 12 | 13.50% | 19.50% |
| 13 | 12.00% | 18.00% |
| 14 | 10.50% | 16.50% |
| 15 | 9.00% | 15.00% |
| 16 | 6.25% | 11.25% |
| 17 | 4.00% | 8.00% |
| 18 | 2.25% | 5.25% |
| 19 | 1.00% | 3.00% |
| 20 | 0.25% | 1.00% |
And here are the graphs for threat 15–20, first without and then with the feat.
Is the feat worth it?
In case of a 50% hit rate with a 15–20/×2 weapon, your critical rate goes up by 6%. That's a 0.06 increase to your damage factor. By contrast, an extra +1 to attacks in general boosts hit rate by 5% and crit rate by 1.5%, resulting in a damage factor boost of 0.065. So the feat is slightly worse than a +1 attack bonus.For a ×3 weapon, once again with a 50% hit rate, the normal damage factor is 0.5 + 0.025 × 2 = 0.55. With Power Critical it goes up to 0.5 + 0.035 × 2 = 0.57. That's only a 0.02 increase. A flat +1 attack bonus results in 0.55 + 0.0275 × 2 = 0.605, a 0.055 increase, which is a lot better than the feat.
Finally, for a 19–20/×4 weapon (a keen scythe), the normal 50% hit-rate damage factor is 0.65. With the feat, it becomes 0.71, while the 55% hit-rate damage factor is 0.715. So in this case the feats is once again slightly weaker than a +1 attack bonus.
Jasper,
I really appreciate the exposition, not to mention AnyDice and the work you've put into it!
:) Thanks, Chuck!